In , K. Kishimoto introduced the notion of P-Galois extensions and gave some fundamental properties of these extensions. P-Galois extensions relate Hopf Galois extensions, and the author treated these topics in . Moreover, the cubic P-Galois extensions over a field were completely determined in . Continuing  and , we classify commutative quartic P-Galois extensions over a field of characteristic not 2.
Galois extension, P-Galois extension, quartic extension
NAKAJIMA, ATSUSHI (2005) "Commutative Quartic P-Galois Extensions Over a Field of Characteristic Not 2," Turkish Journal of Mathematics: Vol. 29: No. 3, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol29/iss3/3